Given that $\lg x=a$ and $\lg y=b$, express $\lg \sqrt{\frac{1000y}{{{x}^{2}}}}$ in terms of $a$ and

Question

Given that $\lg x=a$ and $\lg y=b$, express $\lg \sqrt{\frac{1000y}{{{x}^{2}}}}$ in terms of $a$ and of $b$. [2] Solve the equation ${{\log }_{4}}p-8{{\log }_{p}}4=2$. [4] State the range of values of $x$ for ${{\log }_{x-1}}\left( 6-x \right)$ to be defined. [1]

Accepted Answer

(a) $\frac{3}{2}+\frac{b}{2}-a$ (b) $p=256\text{ or }p=\frac{1}{16}$ (c) $1<x<2\text{ or }2<x<6$

2020 BGSS AM S4 P2 Q1

2020 BGSS AM S4 P2 Q1

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